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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Hyperbolic Lattices and Two-Dimensional Yang-Mills Theory.

G Shankar¹, Joseph Maciejko^1,2

¹Department of Physics, <a href="https://ror.org/0160cpw27">University of Alberta</a>, Edmonton, Alberta T6G 2E1, Canada.

Physical Review Letters

|October 18, 2024

Summary

This summary is machine-generated.

Researchers reconciled discrepancies in analyzing hyperbolic lattices, a synthetic quantum matter. Moments of the density of states in hyperbolic tight-binding models precisely match quantum gauge theory Wilson loops in the large-N limit.

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Area of Science:

Quantum Physics
Condensed Matter Physics
Network Science

Background:

Hyperbolic lattices are synthetic quantum systems with unique properties.
Existing real-space and reciprocal-space methods for analyzing hyperbolic lattices show discrepancies.
Reconciling these methods is crucial for understanding hyperbolic quantum matter.

Purpose of the Study:

To bridge the gap between real-space and reciprocal-space analyses of hyperbolic lattices.
To establish a theoretical framework connecting hyperbolic band theory with quantum gauge theory.
To provide a precise method for calculating energy spectra in hyperbolic systems.

Main Methods:

Establishing an equivalence between hyperbolic band theory and U(N) topological Yang-Mills theory on higher-genus Riemann surfaces.
Connecting moments of the density of states in hyperbolic tight-binding models to Wilson loop expectation values.
Utilizing the large-N limit for exact correspondence.

Main Results:

Demonstrated an exact correspondence between hyperbolic band theory and topological Yang-Mills theory.
Showed that density of states moments in hyperbolic lattices equal Wilson loop expectation values.
Achieved exactness of this correspondence in the large-N limit.

Conclusions:

The study successfully reconciles conflicting methods for analyzing hyperbolic lattices.
A novel connection between condensed matter physics and quantum field theory is established.
This work provides a powerful tool for the study of synthetic quantum matter.